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An ideal gas undergoes isothermal compression from $5 m^{3}$ to $1 m^{3}$ against a constant external pressure of $4 N m^{- 2}$ . Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is $24 J m o l^{- 1} K^{- 1}$ , the temperature of Al increase by

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$\frac{3}{2} K$

$2 K$

$\frac{2}{3} K$

$1 K$

answer is C.

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Detailed Solution

We know that, $w = - P_{e x t} (V_{f} - V_{i})$

$w = - 4 N m^{- 2} (1 - 5) m^{3} w = 16 N m \Rightarrow 16 J$

For isothermal compression, $Δ U = q + w$

$\Rightarrow q = - w = - 16 J (∵ Δ U = 0 f o r i s o t h e r m a l p r o c e s s)$

From calorimetry, Heat given $= n C Δ T$

So, $16 = \frac{1 \times 24 J \times Δ T}{m o l K}$

$∴$ change in temperature, $Δ T = \frac{2}{3} K$

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